Data from: Muscle–spring dynamics in time-limited, elastic movements

Muscle contractions that load in-series springs with slow speed over a long duration do maximal work and store the most elastic energy. However, time constraints, such as those experienced during escape and predation behaviours, may prevent animals from achieving maximal force capacity from their muscles during spring-loading. Here, we ask whether animals that have limited time for elastic energy storage operate with springs that are tuned to submaximal force production. To answer this question, we used a dynamic model of a muscle–spring system undergoing a fixed-end contraction, with parameters from a time-limited spring-loader (bullfrog: Lithobates catesbeiana) and a non-time-limited spring-loader (grasshopper: Schistocerca gregaria). We found that when muscles have less time to contract, stored elastic energy is maximized with lower spring stiffness (quantified as spring constant). The spring stiffness measured in bullfrog tendons permitted less elastic energy storage than was predicted by a modelled, maximal muscle contraction. However, when muscle contractions were modelled using biologically relevant loading times for bullfrog jumps (50 ms), tendon stiffness actually maximized elastic energy storage. In contrast, grasshoppers, which are not time limited, exhibited spring stiffness that maximized elastic energy storage when modelled with a maximal muscle contraction. These findings demonstrate the significance of evolutionary variation in tendon and apodeme properties to realistic jumping contexts as well as the importance of considering the effect of muscle dynamics and behavioural constraints on energy storage in muscle–spring systems.以慢速长时程方式为串联弹簧（in-series springs）加载的肌肉收缩，可产生最大功并储存最多的弹性势能。然而，诸如逃逸与捕食行为中遭遇的时间限制，可能会使动物在弹簧加载过程中无法发挥肌肉的最大出力能力。本研究旨在探讨：弹性储能时长受限的动物，是否会采用适配次最大出力的弹簧系统。为解答这一问题，我们采用了固定端收缩模式下的肌肉-弹簧系统动力学模型，参数分别取自两类依赖弹簧加载的物种：受时间限制的美洲牛蛙（Lithobates catesbeiana），以及不受时间限制的沙漠蝗（Schistocerca gregaria）。我们的研究结果显示，当肌肉收缩的可用时长越短时，采用更低的弹簧刚度（以劲度系数量化）即可实现弹性储能的最大化。相较于模拟最大肌肉收缩时的理论预测值，美洲牛蛙肌腱中实测的弹簧刚度所能储存的弹性势能更少。但当我们采用与美洲牛蛙跳跃行为匹配的生物学合理加载时长（50毫秒）来模拟肌肉收缩时，肌腱刚度反而实现了弹性储能的最大化。与之形成对比的是，不受时间限制的沙漠蝗，其弹簧刚度在以最大肌肉收缩模拟时，即可实现弹性储能的最大化。本研究结果证实了肌腱与表皮内突（apodeme）特性的进化变异在真实跳跃场景中的重要意义，同时也凸显了在肌肉-弹簧系统中，考虑肌肉动力学与行为约束对储能影响的必要性。